Passive Covert Radars using CP-OFDM SFN. Reference signal recovery from blind beamforming

A passive Coherent Location (PCL) system uses the signal transmitted by so called illuminators-of-opportunity in the environment for the illumination of targets. It is then necessary to recover the original transmitted signal to be compared to the targets echoes. With CP-OFDM transmissions, it is quite easy to recover the original data and then to reconstruct the original transmission. But in the case of a Single Frequency Network , characterized by the presence of several transmitters using the same carrier frequency to broadcast the same signal, it is necessary to use directional sensors or spatial filter. In this paper, we propose two blind solutions : classical beamforming and CAPON filtering. Results of real measurements are presented

Séparation autodidacte de sources temporellement corrélées

La méthode de séparation aveugle, proposée dans le cadre de mélange instantané de sources indépendantes, est basée sur la recherche de solutions d'un système linéaire aux valeurs propres : MX = λRX. On montre que, si l'on choisit la matrice R égale à la matrice M(2k), dérivée 2kième de la matrice d'intercovariance M des observations, on assure l'obtention d'une solution par une méthodologie robuste et stable. On présente des simulations dans des situations défavorables telles que le mélange de sources gaussiennes aux fonctions de corrélations proches

A compact sensor array for blind separation of sources

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Adaptive Target Detection Techniques for OFDM-Based Passive Radar Exploiting Spatial Diversity

International audienceRecently, it has been studied the benefit of using a channel-based detector (CHAD) with a passive radar exploiting OFDM waveforms radiated e.g. by DVB-T transmitters of opportunity. When multiple antennas are available on receive, we state that CHAD can be seen as space-time array-processing performing on a particular coherent frequency datacube. Building on this new interpretation, we propose an improved version of CHAD in the form of a fully dimensional space-time adaptive processing. Optimization of the signal-to-interference-plus-noise ratio is obtained combining a linearly constrained minimum variance (LCMV) space-time adaptive beamforming and a least squares (LS) spatial adaptive filtering. Unlike classical STAP approaches, no training data are here used and only one space-time sample matrix inversion is required. The computational load is then highly reduced allowing a practical deployment. Moreover, since no beamscan in space is performed, the knowledge of array characteristics is not required and the performance shall not be impacted by any calibration errors. Finally, the full set of target signal returns being collected in a single range-Doppler surveillance map, the detection process is then simplified. Results on experimental data show the interests of this new surveillance scheme: no need for a prior rejection of the dominant interference, systematic reduction of secondary lobes, discrimination of slow moving targets

The Archimedes principle applied to separation of uniformly distributed sources

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BLIND WAVE SEPARATION BY SPATIAL OVERSAMPLING

International audienceThis paper is a contribution to the problem of the separation of propagating source signals recorded simultaneously by a s e t of receivers. We propose to use a small-sized sensor array so that the waves are spatially oversampled. Sensors are assumed to be directional, to have the same complex frequency response and to be diierently oriented in space. Under these assumptions, sources are received on each sensor with diierent attenuations and with diierent time delays. When the dimensions of the array are chosen so that time delays are small in comparison with the coherence time of each source, we s h o w that the array outputs can be approximated to a particular model of instantaneous mixtures involving the sources and their rst derivative with respect to time. Because sources are statistically dependent to their rst derivative, this problem does not appear as a classical Blind Source Separation (BSS) problem. We present then a matched second-order blind identiication algorithm in order to estimate this particular mixing system. The validity of the proposed model and of our algorithm is connrmed by computer simulations in the case of audio sources. 1. GENERAL MODEL It is assumed that a set of N independent colored signals x 1 (t) : : : x N (t) are propagating in an echo-free environment. These signals are recorded on M sensors without any additive noise (presence of noise will be treated in the full paper). The observation satisfy the equation model below: y 1 (t) = x 1 (t) + x 2 (t) + : : : + x N (t) y i (t) = j=N X j=1 c iij x j (t ; iij) i = 2 : : : M (1) where iij and c iij represent respectively the relative delay and the relative amplitude of source x j (t) observed on the i th sensor versus the rst observation y 1 (t). We'll show in the full paper that in case of a compact sensor array, delays are suuciently small when: 2 iij << 1 2 2 2 M 8ii jj where M is the maximum frequency present in the observations. In this case, an approximation for the observations y i (t) (i = 2 : : : M) using an order one Taylor expansion can be considered: y i (t) c ii1 x 1 (t) ; c ii1 ii1 dx 1 (t) dt + c ii2 x 2 (t) ; c ii2 ii2 dx 2 (t) dt + : : : + c iiN x N (t) ; c iiN iiN dx N (t) dt : (2) Let consider the observation vector y(t) = y 1 (t) y 2 (t) : : : y N (t)] T. Using approximation (2) in (1), the set of equations (1) can be rewritten as: y(t) M 1 x(t) + M 2 _ x(t): where

Second-Order Blind Source Separation: A New Expression of Instantaneous Separating Matrix for Mixtures of Delayed Sources

International audienceIn this paper, we study the blind separation of mixtures of propagating waves (delayed sources) encountered for example in underwater telephone (UWT) systems. We suggest a new second-order statistics method using as many observations as sources. First, we show that each of the N delayed sources can be developed as a particular linear combination of the different temporal-derivatives of the N observations. Under some assumptions, an instantaneous rectangular separating matrix is then identified by the joint diagonalization of a set of covariance matrices estimated from the observations and its derivatives. The algorithm used takes into account the particular structure of the spectral mixing matrix encountered. A numerical simulation is provided in a 3-sources/3-observations case for propagating audio signals

BLIND WAVE SEPARATION BY SPATIAL OVERSAMPLING

International audienceThis paper is a contribution to the problem of the separation of propagating source signals recorded simultaneously by a s e t of receivers. We propose to use a small-sized sensor array so that the waves are spatially oversampled. Sensors are assumed to be directional, to have the same complex frequency response and to be diierently oriented in space. Under these assumptions, sources are received on each sensor with diierent attenuations and with diierent time delays. When the dimensions of the array are chosen so that time delays are small in comparison with the coherence time of each source, we s h o w that the array outputs can be approximated to a particular model of instantaneous mixtures involving the sources and their rst derivative with respect to time. Because sources are statistically dependent to their rst derivative, this problem does not appear as a classical Blind Source Separation (BSS) problem. We present then a matched second-order blind identiication algorithm in order to estimate this particular mixing system. The validity of the proposed model and of our algorithm is connrmed by computer simulations in the case of audio sources. 1. GENERAL MODEL It is assumed that a set of N independent colored signals x 1 (t) : : : x N (t) are propagating in an echo-free environment. These signals are recorded on M sensors without any additive noise (presence of noise will be treated in the full paper). The observation satisfy the equation model below: y 1 (t) = x 1 (t) + x 2 (t) + : : : + x N (t) y i (t) = j=N X j=1 c iij x j (t ; iij) i = 2 : : : M (1) where iij and c iij represent respectively the relative delay and the relative amplitude of source x j (t) observed on the i th sensor versus the rst observation y 1 (t). We'll show in the full paper that in case of a compact sensor array, delays are suuciently small when: 2 iij << 1 2 2 2 M 8ii jj where M is the maximum frequency present in the observations. In this case, an approximation for the observations y i (t) (i = 2 : : : M) using an order one Taylor expansion can be considered: y i (t) c ii1 x 1 (t) ; c ii1 ii1 dx 1 (t) dt + c ii2 x 2 (t) ; c ii2 ii2 dx 2 (t) dt + : : : + c iiN x N (t) ; c iiN iiN dx N (t) dt : (2) Let consider the observation vector y(t) = y 1 (t) y 2 (t) : : : y N (t)] T. Using approximation (2) in (1), the set of equations (1) can be rewritten as: y(t) M 1 x(t) + M 2 _ x(t): where

An instantaneous formulation of mixtures for blind separation of propagating waves

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Passive Covert Radars using CP-OFDM signals. A new efficient method to extract targets echoes

Passive Coherent Location (PCL) systems use the signal transmitted by so called illuminators-of-opportunity in the environment to illuminates the targets. With CP-OFDM transmissions, it is quite easy to recover the original data and then to reconstruct the original transmission. The main difficulty is to extract, from the mixture received on the sensors, only the targets echoes. A new efficient and low complexity method is exposed here. Results on both simulated and real data are presented